Potential of interaction between two- and three-dimensional solitons

A general method to find an effective potential of interaction between far separated two-dimensional (2D) and 3D solitons is elaborated, including the case of 2D vortex solitons. The method is based on explicit calculation of the overlapping term in the full Hamiltonian of the system (without assuming that the “tail” of each soliton is not affected by its interaction with the other soliton). The result is obtained in an explicit form that does not contain an artificially introduced radius of the overlapping region. The potential applies to spatial and spatiotemporal solitons in nonlinear optics, where it helps to solve various dynamical problems: collisions, formation of bound states (BS’s), etc. In particular, an orbiting BS of two solitons is always unstable. In the presence of weak dissipation and gain, the effective potential can also be derived, giving rise to bound states similar to those recently studied in 1D models.